Which measure of central tendency is most affected by a skewed distribution?

The mean is the measure of central tendency that is most affected by a skewed distribution. This is because the mean is calculated by summing all the values in a dataset and dividing by the number of values. Therefore, it takes into account every data point and gets pulled in the direction of the skew. In a positively skewed distribution, where a few high values are present, the mean will be higher than the median and mode, reflecting those extreme values. Conversely, in a negatively skewed distribution with a few low values, the mean will be lower than the median and mode.

In contrast, the median, which is the middle value when data is ordered, is much less affected by extreme values because it only depends on the central point of the dataset rather than all values. The mode, being the most frequently occurring value, remains unchanged by the presence of outliers or skewed data in many cases, making it the least affected by skewness. Therefore, the mean is the measure of central tendency that best reflects the impact of skewness in a distribution.